FIG. 1a shows a simple model for a field effect transistor (FET) 100. An FET typically has three terminals 101, 102, 103 and is typically viewed as having two basic modes of operation: “linear”; and, “saturation”. Both the linear and velocity saturation regions are observed in the exemplary FET transfer characteristics that are presented in FIG. 1b. 
According to a perspective of an FET's linear and saturation regions of operation, the first terminal 101 is used to influence the number of free carriers that are present within a conductive channel 104. The current through the conductive channel 104 is approximately proportional to the number of these free carriers multiplied by their effective velocity through the conductive channel 104.
Over the course of the FET's “linear” region of operation, which is approximately region 105 of FIG. 1b, a voltage established across the second and third terminals 102, 103 (V23) determines the current that flows through the conductive channel (I23). By contrast, over the course of the FET's “saturation” region of operation, which is approximately region 106 of FIG. 1b, the current I23 that flows through the conductive channel 104 is essentially “fixed” because the conductive channel's ability to transport electrical current is “saturated” (e.g., the velocity of the conductive channel's free carriers reach an internal “speed limit”). Traditionally, one of terminals 102 and 103 is called a “source” and the other of terminals 102 and 103 is called a “drain”.
Recent publications have disclosed FETs that employ a Carbon Nanotube (CNT) as the conductive channel 104. A Carbon nanotube (CNT) can be viewed as a sheet of graphite (also known as graphene) that has been rolled into the shape of a tube (end capped or non-end capped). CNTs having certain properties (e.g., a “metallic” CNT having electronic properties akin to a metal) may be appropriate for certain applications while CNTs having certain other properties (e.g., a “semiconducting” CNT having electronic properties akin to a semiconductor) may be appropriate for certain other applications. CNT properties tend to be a function of the CNT's “chirality” and diameter. The chirality of a CNT characterizes its arrangement of carbon atoms (e.g., arm chair, zigzag, helical/chiral). The diameter of a CNT is the span across a cross section of the tube.
FIG. 2a shows a basic outline for a transistor designed to use a CNT 204 as its conductive channel. According to the transistor design of FIG. 2a, a metal source electrode 202 makes contact to a CNT 204 at contact region 204a, and, a metal drain electrode 203 makes contact to CNT 204 at contact region 204b. The transistor also includes a gate electrode 201. In implementation, the CNT 204 is expected to have electrical conducting properties sufficient for the gate electrode 201 to be used as a basis for influencing the number of free carriers that appear in the CNT 204 so that the magnitude of the current that flows through the CNT can be modulated at the gate node 201.
However, a transistor designed according to the approach of FIG. 2a, due to an “ambipolar conduction” problem, will exhibit excessive current through the CNT conductive channel 204 when the transistor is supposed to be “off”. FIG. 2b shows an energy band diagram across the length of the CNT 204 when a VDS voltage of reasonable magnitude is applied across the drain and source electrodes while the transistor is “off”. When the transistor is off, ideally, no current flows through the CNT. However, the VDS voltage “thins” the Schottky barriers 210, 220 formed at contact regions 204a and 204b, respectively, so as to promote tunneling into the CNT. Specifically, for n type FETs, holes tunnel through the drain Schottky barrier 220. These carriers then traverse the length of the CNT conductive channel 204 resulting in current that is unacceptably high for an “off” transistor.